Spin transport of a doped Mott insulator in moiré heterostructures.

Moiré superlattices of semiconducting transition metal dichalcogenide heterobilayers are model systems for investigating strongly correlated electronic phenomena. Specifically, WSe/WS moiré superlattices have emerged as a quantum simulator for the two-dimensional extended Hubbard model. Experimental studies of charge transport have revealed correlated Mott insulator and generalized Wigner crystal states, but spin transport of the moiré heterostructure has not yet been sufficiently explored. Here, we use spatially and temporally resolved circular dichroism spectroscopy to directly image the spin transport as a function of carrier doping and temperature in WSe/WS moiré heterostructures. We observe diffusive spin transport at all hole concentrations at 11 Kelvin - including the Mott insulator at one hole per moiré unit cell - where charge transport is strongly suppressed. At elevated temperatures the spin diffusion constant remains unchanged in the Mott insulator state, but it increases significantly at finite doping away from the Mott state. The doping- and temperature-dependent spin transport can be qualitatively understood using a t-J model, where spins can move via the hopping of spin-carrying charges and via the exchange interaction.